Bloch Domain Walls Research Articles

Analytical Representation of the Vortex Structure of a Bloch Domain Wall

An analytical method for determining the vertical asymmetric magnetization distribution in a two-dimensional Bloch domain wall (DW) is proposed in this work. An asymmetric two-dimensional magnetization distribution in a DW is obtained using simple analytical dependences with a minimum number of variable parameters. The structure and energy of the Bloch DW in permalloy-type magnetic films are studied for a wide range of film thickness. The calculation results are compared with the calculation results of other authors.

Domain Structure of Hexaferrite BaFe12O19 Near the Curie Temperature

The features of the structure of domain walls in hexaferrite BaFe12O19 have been studied near the Curie temperature TC = 724 K. The studies have been performed on the single-crystal samples in ac magnetic field with frequencies of 73 MHz and 71 MHz, and in dc magnetic field in the range 0–0.25 kOe. In BaFe12O19 at temperature T1 = 716 K, the magnetic structure of domain walls is changed: the Bloch walls change into linear walls as temperature increases. The value of ΔT = TC – T1 ≈ 8 K. The physical mechanism considered in this work and determining the difference of temperature ranges of existence a magnetically ordered state and the temperature range of existence of the Bloch domain walls agrees with the experimental results. Estimation of the criterion of the Bloch domain wall transition to a linear wall at T1 = 716 K agrees with the obtained experimental data.

On the statics and dynamics of transverse domain walls in bilayer piezoelectric-magnetostrictive nanostructures

In this article, we investigate the static and dynamic properties of transverse Bloch domain wall in an isotropic, linearly elastic bilayer piezoelectric-magnetostrictive nanostructures under the influence of axial (driving), transverse magnetic fields and spin-polarized electric current. To be precise, we perform the analysis under the framework of the one-dimensional Extended Landau–Lifshitz–Gilbert equation in the presence of stresses generated by a piezoelectric actuator. First, we derive the magnetization profile in the two distant domains and then study the static magnetization profile in the sole presence of the applied transverse magnetic field. Next, we propose a new Walker’s type trial function and establish the analytical expressions of the dynamical quantities such as moving DW profile, velocity, displacement, and excitation angle by using a small angle approximation approach. Finally, we delineate the obtained analytical results with the aid of numerical illustrations.

Особенности доменной структуры гексаферрита BaFe-=SUB=-12-=/SUB=-O-=SUB=-19-=/SUB=- вблизи температуры Кюри

The structural features of the domain walls of the BaFe12O19 hexaferrite near the Curie temperature TC = 724 K were studied. The studies were performed on single-crystal samples in an alternating magnetic field with a frequency of 73 MHz and 71 MHz with a constant magnetic field in the range 0–0.25 kOe. In BaFe12O19 at a temperature of T1 = 716 K, the magnetic structure of the domain walls changes – the Bloch walls transform into linear walls with increasing temperature. The value ΔТ = Tc – T1≈8 K. The physical mechanism considered in the work, which determines the difference between the temperature range of the existence of the magnetically ordered state and the temperature range of the existence of the Bloch domain walls, is consistent with experimental results. The estimated calculation of the criterion for the transition of the Bloch domain wall to a linear wall at T1 = 716 K corresponds to the obtained experimental data.

Topological excitations in rotating Bose-Einstein condensates with Rashba-Dresselhaus spin-orbit coupling in a two-dimensional optical lattice

We study the ground-state configurations and spin textures of rotating two-component Bose-Einstein condensates (BECs) with Rashba-Dresselhaus spin-orbit coupling (RD-SOC), which are confined in a two-dimensional (2D) optical lattice plus a 2D harmonic trap. In the absence of rotation, a relatively small isotropic 2D RD-SOC leads to the generation of ghost vortices for initially miscible BECs, while it gives rise to the creation of rectangular vortex-antivortex lattices for initially immiscible BECs. As the strength of the 2D RD-SOC enhances, the visible vortices or the 2D vortex-antivortex chains are created for the former case, whereas the rectangular vortex-antivortex lattices are transformed into vortex-antivortex rings for the later case. For the initially immiscible BECs with fixed 2D RD-SOC strength, the increase of rotation frequency can result in the structural phase transition from square vortex lattice to irregular triangular vortex lattice and the system transition from initial phase separation to phase mixing. In addition, we analyze the combined effects of 1D RD-SOC and rotation on the vortex configurations of the ground states for the case of initial phase separation. The increase of 1D SOC strength, rotation frequency or both of them may result in the formation of vortex chain and phase mixing. Furthermore, the typical spin textures for both the cases of 2D RD-SOC and 1D RD-SOC are discussed. It is shown that the system favors novel spin textures and skyrmion configurations including an exotic skyrmion-half-skyrmion lattice (skyrmion-meron lattice), a complicated meron lattice, a skyrmion chain, and a Bloch domain wall.

An Analytical Way of Determining the Vortex Structure of a Bloch Domain Wall

A way of creating analytical models that describe the distribution of vortex magnetization in a two-dimensional Bloch domain wall (DW) is proposed, based on a system of equations for the line of transition. The structure and energy of Bloch DWs in thin magnetic permalloy-type films are studied at a film thickness of 100 nm. The results from calculations are compared to those of other authors.

Lorentz TEM investigation of chiral spin textures and Néel Skyrmions in asymmetric [Pt/(Co/Ni)M/Ir]N multi-layer thin films

We examine magnetic domain patterns in symmetric [Co/Ni]$_M$ and asymmetric [Pt/(Co/Ni)$_M$/Ir]$_N$ multi-layers using Fresnel mode Lorentz transmission electron microscopy (LTEM). In the symmetric multi-layer, where the Dzyaloshinskii-Moriya Interaction is expected to be zero, we observe purely Bloch type domain walls with no preferred chirality. In the asymmetric multi-layers, where significant interfacial DMI is present, we observe domain patterns with chiral N\'eel domain walls, which evolve into sub-100nm isolated N\'eel Skyrmions with the application of a perpendicular field. The impact of layer thickness and film stack on interfacial magnetic properties is discussed in the context of developing a tunable multi-layer system for future spintronic applications.

Domain wall induced modulation of low field H-T phase diagram in patterned superconductor-ferromagnet stripes

We present a systematic study of the magnetic domain wall induced modulation of superconducting transition temperature (Tc) in Nb/Ni bilayer stripes. By varying the thickness of the Ni layer from 20 nm to 100 nm we have been able to measure the low field Tc-H phase diagram spanning the Néel domain wall and Bloch domain wall range of thicknesses. Micromagnetic simulations confirmed a stronger out-of-plane stray field in the Bloch domain walls compared to the Néel walls. A suppression in Tc was observed in the magnetization reversal region of the Ni film, the magnitude of which followed linearly to the strength of the out-of-plane stray field due to the domain walls. The upper limit of the magnitude of domain wall stray field was roughly estimated by comparing the Tc of the suppressed region of H-Tc phase diagrams with the unaffected part of the H-Tc curve. With Bloch domain walls a change in Tc of more than 60 mK was observed which is much more compared to the earlier reports. We believe that the narrow stripe geometry of the bilayers and the transverse external field maximized the effect of the domain walls in the Ni layer on the overlying superconducting film, leading to a larger change in Tc. This observation may be useful for domain wall controlled switching devices in superconducting spintronics.

Inelastic Spin‐Wave Scattering by Bloch Domain Wall Flexure Oscillations

The calculations of the inelastic spin wave scattering by flexure vibrations of the Bloch domain wall (Winter's magnons) in thin magnetic films are presented. The approach is based on the interaction of the propagating spin waves with the dynamical emergent electromagnetic field generated by the moving inhomogeneous magnetization texture (domain wall). The probability of the spin wave scattering for the Winter's magnon emission and absorption processes essentially rises with the spin wave scattering angle increase up to 90°. The angular dependence of the scattering probability is essentially stronger for the magnon absorption processes that allow distinguishing these elementary emission/absorption processes experimentally.

Cavity optomechanics of topological spin textures in magnetic insulators

Collective dynamics of topological magnetic textures can be thought of as a massive particle moving in a magnetic pinning potential. We demonstrate that inside a cavity resonator this effective mechanical system can feel the electromagnetic radiation pressure from cavity photons through the magneto-optical inverse Faraday and Cotton-Mouton effects. We estimate values for the effective parameters of the optomechanical coupling for two spin textures -- a Bloch domain wall and a chiral magnetic soliton lattice. The soliton lattice has magnetic chirality, so that in circularly polarized light it behaves like a chiral particle with the sign of the optomechanical coupling determined by the helicity of the light and chirality of the lattice. Most interestingly, we find a level attraction regime for the soliton lattice, which is tunable through an applied magnetic field.

Influence of a Domain Wall on the Spin Polarization of Electric Current

The spin polarization of charge carriers moving in a ferromagnet through a 180° Bloch domain wall is calculated. It is demonstrated that a magnetization component parallel to the electric current and proportional to its strength emerges after the passage through a wall.

Sudden magnetization drops in superconductor/ferromagnet bilayered structures

We report in-plane magnetization measurements on Nb/Co bilayers using a thin superconductor Nb ∼ 25 nm and a thick ferromagnet Co ∼ 40−55 nm where Bloch domain walls (BDW) are energetically favorable. Here sharp drops in the magnetization are explained as direct consequence of BDW stray fields that induce vortices in the out of plane direction. These are generated at small fields around the coercive field of the ferromagnet and removed at large fields of the order of Hc2. These two well distinctive magnetic states of the superconductor, with or without out of plane vortices, is the same mechanism used to explain the drops in critical currents reported in Patiño et al (2009 Eur. Phys. J. B 68 73).

Pinning of a ferroelectric Bloch wall at a paraelectric layer.

The phase-field simulations of ferroelectric Bloch domain walls in BaTiO3–SrTiO3 crystalline superlattices performed in this study suggest that a paraelectric layer with a thickness comparable to the thickness of the domain wall itself can act as an efficient pinning layer. At the same time, such a layer facilitates the possibility to switch domain wall helicity by an external electric field or even to completely change the characteristic structure of a ferroelectric Bloch wall passing through it. Thus, ferroelectric Bloch domain walls are shown to be ideal nanoscale objects with switchable properties. The reported results hint towards the possibility to exploit ferroelectric domain wall interaction with simple nanoscale devices.

Material Developments and Domain Wall-Based Nanosecond-Scale Switching Process in Perpendicularly Magnetized STT-MRAM Cells

We investigate the Gilbert damping and the magnetization switching of perpendicularly magnetized FeCoB-based free layers embedded in tunnel junctions adequate for spin-torque operated memories. We study the influence of the boron content in MgO / FeCoB /Ta systems alloys on their Gilbert damping after crystallization annealing. Increasing the boron content from 20 to 30\% increases the crystallization temperature, thereby postponing the onset of elemental diffusion within the free layer. This reduction of the interdiffusion of the Ta atoms helps maintaining the Gilbert damping at a low level of 0.009 without any penalty on the anisotropy and the magneto-transport properties up to the 400$^\circ$C annealing required in CMOS back-end of line processing. In addition, we show that dual MgO free layers of composition MgO/FeCoB/Ta/FeCoB/MgO have a substantially lower damping than their MgO/FeCoB/Ta counterparts, reaching damping parameters as low as 0.0039 for a 3 \r{A} thick Tantalum spacer. This confirms that the dominant channel of damping is the presence of Ta impurities within the FeCoB alloy. On optimized tunnel junctions, we then study the duration of the switching events induced by spin-transfer-torque. We focus on the sub-threshold thermally activated switching in optimal applied field conditions. From the electrical signatures of the switching, we infer that once the nucleation has occurred, the reversal proceeds by a domain wall sweeping though the device at a few 10 m/s. The smaller the device, the faster its switching. We present an analytical model to account for our findings. The domain wall velocity is predicted to scale linearly with the current for devices much larger than the wall width. The wall velocity depends on the Bloch domain wall width, such that the devices with the lowest exchange stiffness will be the ones that host the domain walls with the slowest mobilities.

Theory of linear spin wave emission from a Bloch domain wall

We report an analytical theory of linear emission of exchange spin waves from a Bloch domain wall, excited by a uniform microwave magnetic field. The problem is reduced to a one-dimensional Schr\"odinger-like equation with a P\"oschl-Teller potential and a driving term of the same profile. The emission of plane spin waves is observed at excitation frequencies above a threshold value, as a result of a linear process. The height-to-width aspect ratio of the P\"oschl-Teller profile for a domain wall is found to correspond to a local maximum of the emission efficiency. Furthermore, for a tailored P\"oschl-Teller potential with a variable aspect ratio, particular values of the latter can lead to enhanced or even completely suppressed emission.

Continuously tuneable critical current in superconductor-ferromagnet multilayers

We demonstrate that the critical current of superconducting Nb/Ni multilayers can be continuously tuned by up to a factor of three during magnetization reversal of the Ni films under an applied in-plane magnetic field. Our observations are in reasonably good agreement with a model of vortex pinning by Bloch domain walls that proliferate in the samples during magnetization reversal, whereby each vortex interacts with at most one wall in any of the Ni layers. Our model suggests ways in which the controllable pinning effect could be significantly enhanced, with important potential applications in tuneable superconducting devices.

Origin of domain wall induced magnetoelectricity in rare-earth iron garnet single crystals and films

ABSTRACTIn this article, we discuss the mechanism of magnetoelectric effect in rare-earth iron garnets related to the low symmetry environment of rare-earth ions and magnetic inhomogeneity created by iron subsystem. Low symmetry environment of rare-earth ions leads to antiferroelectric arrangement of their electric dipole moments and favors releasing of iron garnets ferroelectricity. Magnetic domain walls act as the sources of non-uniform effective magnetic field breaking antiferroelectric ordering. We calculate electric polarization in a vicinity of Bloch domain walls in rare-earth iron garnet crystals and films, pick out their distinguished features, and touch upon experimental evidences of domain wall induced magnetoelectricity.

A Combined TEM/STEM and Micromagnetic Study of the Anisotropic Nature of Grain Boundaries and Coercivity in Nd-Fe-B Magnets

The nanoanalytical high resolution TEM/STEM investigation of the intergranular grain boundary phase of anisotropic sintered and rapidly quenched heavy rare earth-free Nd-Fe-B magnet materials revealed a difference in composition for grain boundaries parallel (large Fe-content) and perpendicular (low Fe content) to the alignment direction. This behaviour vanishes in magnets with a high degree of misorientation. The numerical finite element micromagnetic simulations are based on the anisotropic compositional behaviour of GBs and show a decrease of the coercive field with an increasing thickness of the grain boundary layer. The magnetization reversal and expansion of reversed magnetic domains primarily start as Bloch domain wall at grain boundaries parallel to thec-axis and secondly as Néel domain wall perpendicular to thec-axis into the adjacent hard magnetic grains. The increasing misalignment of grains leads to the loss of the anisotropic compositional behaviour and therefore to an averaged value of the grain boundary composition. In this case the simulations show an increase of the coercive field compared to the anisotropic magnet. The calculated coercive field values of the investigated magnet samples are in the order ofμ0HcJ=1.8 T–2.1 Tfor a mean grain boundary thickness of 4 nm, which agrees perfectly with the experimental data.

Nanocompositional Electron Microscopic Analysis and Role of Grain Boundary Phase of Isotropically Oriented Nd-Fe-B Magnets

Nanoanalytical TEM characterization in combination with finite element micromagnetic modelling clarifies the impact of the grain misalignment and grain boundary nanocomposition on the coercive field and gives guidelines how to improve coercivity in Nd-Fe-B based magnets. The nanoprobe electron energy loss spectroscopy measurements obtained an asymmetric composition profile of the Fe-content across the grain boundary phase in isotropically oriented melt-spun magnets and showed an enrichment of iron up to 60 at% in the Nd-containing grain boundaries close to Nd2Fe14B grain surfaces parallel to the c-axis and a reduced iron content up to 35% close to grain surfaces perpendicular to the c-axis. The numerical micromagnetic simulations on isotropically oriented magnets using realistic model structures from the TEM results reveal a complex magnetization reversal starting at the grain boundary phase and show that the coercive field increases compared to directly coupled grains with no grain boundary phase independently of the grain boundary thickness. This behaviour is contrary to the one in aligned anisotropic magnets, where the coercive field decreases compared to directly coupled grains with an increasing grain boundary thickness, if Js value is > 0.2 T, and the magnetization reversal and expansion of reversed magnetic domains primarily start as Bloch domain wall at grain boundaries at the prismatic planes parallel to the c-axis and secondly as Néel domain wall at the basal planes perpendicular to the c-axis. In summary our study shows an increase of coercive field in isotropically oriented Nd-Fe-B magnets for GB layer thickness > 5 nm and an average Js value of the GB layer < 0.8 T compared to the magnet with perfectly aligned grains.

Classification of magnetic inhomogeneities and0−πtransitions in superconducting-magnetic hybrid structures

We present a comparative study of pair correlations and currents through superconducting-magnetic hybrid systems with a particular emphasis on the tunable Bloch domain wall of an exchange spring. This study of the Gor'kov functions contrasts magnetic systems with domain walls that change at discrete points in the magnetic region with those that change continuously throughout. We present results for misaligned homogeneous magnetic multilayers, including spin valves, for discrete domain walls, as well as exchange springs and helical domain walls --such as Holmium-- for the continuous case. Introducing a rotating basis to disentangle the role of singlet and triplet correlations, we demonstrate that substantial amounts of (so-called short range) singlet correlations are generated throughout the magnetic system in a continuous domain wall via the cascade effect. We propose a classification of $0-\pi$ transitions of the Josephson current into three types, according to the predominant pair correlations symmetries involved in the current. Properties of exchange springs for an experimental study of the proposed effects are discussed. The interplay between components of the Gor'kov function that are parallel and perpendicular to the local magnetization lead to a novel prediction about their role in a proximity system with a progressively twisting helix that is experimentally measurable.